MATLAB代码 信号分析 VMD分解代码 包络谱分析

function [varargout] = vmd(x,varargin) %VMD Variational mode decomposition % [IMF,RESIDUAL] = VMD(X) returns intrinsic mode functions (IMFs) and a % residual signal corresponding to the variational mode decomposition % (VMD) of X, with default decomposition parameters. X can be a vector or % a timetable with a single variable containing a vector. X must be a % real signal. When X is a vector, IMF is a matrix where each column % stores an extracted intrinsic mode function, and RESIDUAL is a column % vector storing the residual. When X is a timetable, IMF is a timetable % with multiple single variables where each variable stores a mode % function, and RESIDUAL is a timetable with a single variable. X can be % double or single precision. % % [IMF,RESIDUAL] = VMD(X,'Name1',Value1,'Name2',Value2,...) % specifies name-value pairs that configure the initial optimization % settings and the decomposition stopping criterion to be used for VMD. % The supported name-value pairs are: % % 'NumIMFs': Number of decomposition IMFs. The default % value is 5. % % 'MaxIterations': Maximum number of optimization iterations. The % optimization process stops when the number of % iterations is greater than MaxIterations. The % default value is 500. % % 'AbsoluteTolerance': Mode convergence tolerance. The optimization % 'RelativeTolerance': process stops when two conditions are met at % the same time: 1) The average squared absolute % improvement toward convergence of IMFs in two % consecutive iterations is less than % AbsoluteTolerance; and 2) The average relative % improvement toward convergence of IMFs in two % consecutive iterations is less than % RelativeTolerance. AbsoluteTolerance and % RelativeTolerance are both specified as % positive real values and default to 5e-6 and % AbsoluteTolerance*1e3, respectively. % % 'CentralFrequencies': Initial central IMF frequencies, specified as % a vector of length NumIMFs. Vector values must % be within the range, [0,0.5] cycles/sample, % which is equivalent to the frequency range, % [0,pi] radians/sample. % % 'InitializeMethod': Method to initialize the central frequencies. % 'CentralFrequencies' and 'InitializeMethod' % are mutually exclusive. The methods can be: % % 'random' - Initialize the central frequencies % as random numbers distributed uniformly in the % interval [0,0.5]. % % 'grid' - Initialize the central frequencies as % a uniformly sampled grid in the interval % [0,0.5]. % % 'peaks' - Initialize the central frequencies % as the peak locations of the signal in the % frequency domain (default). % % 'InitialIMFs': Initial IMFs, specified as a real matrix with % rows corresponding to time samples and columns % corresponding to modes. The default value is a % matrix of zeros. % % 'PenaltyFactor': Penalty factor for reconstruction fidelity, % specified as a positive real value. The % smaller its the value, the stricter the data % fidelity. The default value is 1000. % % 'InitialLM': Initial frequency-domain Lagrange multiplier % over the interval, [0,0.5]. The multiplier % enforces the reconstruction constraint. The % default value is a complex vector of zeros. % The length of the multiplier depends on the % input size. See documentation for more % details. % % 'LMUpdateRate': Update rate for the Lagrange multiplier in % each iteration. A higher rate results in % faster convergence but increases the chance of % getting stuck in a local optimum. The default % value is 0.01. % % 'Display': Set to true to display the average absolute % and relative improvement of modes and central % frequencies every 20 iterations, and show the % final stopping information. The default is % false. % % [IMF,RESIDUAL,INFO] = VMD(...) returns the IMFs, the residual, and a % structure containing these fields: % % ExitFlag: Termination flag. A value of 0 indicates the % algorithm stopped when it reached the maximum % number of iterations. A value of 1 indicates % the algorithm stopped when it met the absolute % and relative tolerances. % % CentralFrequencies: Central frequencies of the IMFs. % % NumIterations: Total number of iterations. % % AbsoluteImprovement: Average squared absolute improvement toward % convergence of the IMFs between the final two % iterations. % % RelativeImprovement: Average relative improvement toward % convergence of the IMFs between the final two % iterations. % % LagrangeMultiplier: Frequency-domain Lagrange multiplier at the % last iteration. % % VMD(...) with no output arguments plots the original signal, the % residual signal, and the IMFs in the same figure. % % % EXAMPLE 1: % % Compute and display the VMD of a signal % t = 0:1e-3:1; % x1 = cos(2*pi*2*t); % x2 = 1/4*cos(2*pi*24*t); % x3 = 1/16*cos(2*pi*288*t); % x = x1 + x2 + x3 + 0.1*randn(1,length(t)); % vmd(x,'NumIMFs',3,'Display',true) % % % EXAMPLE 2: % % Compute the VMD of a signal and output decomposition details. % % Check that the summation of the IMFs and the residual returns the % % original signal % t = 0:1e-3:4; % x1 = sin(2*pi*50*t) + sin(2*pi*200*t); % x2 = sin(2*pi*25*t) + sin(2*pi*100*t) + sin(2*pi*250*t); % x = [x1 x2] + 0.1*randn(1,length(t)*2); % [IMFs,residual,info] = vmd(x,'MaxIterations',600); % max(x(:) - (sum(IMFs,2)+residual)) % % See also HHT and EMD. % % Copyright 2019-2022 The MathWorks, Inc. %#codegen signalwavelet.internal.licenseCheck; %--------------------------------- % Check inputs/outputs narginchk(1,23); if coder.target('MATLAB') % for MATLAB nargoutchk(0,3); else nargoutchk(1,3); end % Parse input [x,td,isTT] = parseInput(x); % Parse name-value pairs opts = signalwavelet.internal.vmd.vmdParser(length(x),class(x),varargin{:}); if isTT coder.internal.assert(coder.internal.isConst(opts.NumIMFs),... 'shared_signalwavelet:vmd:vmd:NeedConstantNumIMFs'); end [IMF,residual,info] = computeVMD(x,opts); if (nargout == 0) && coder.target('MATLAB') signalwavelet.internal.convenienceplot.imfPlot(x,IMF,residual,td,'vmd'); end if nargout > 0 if isTT variableNames = cell(1,opts.NumIMFs); coder.unroll(); for i = 1:opts.NumIMFs var